The series is to be approximated by partial sums

MATHEMATICS · Subjective · AP · Calculus BC · Infinite Sequences and Series · Infinite Sequences and Series

Problem

The series ∑n=0∞(−1)nn+3(n+1)2\displaystyle\sum_{n=0}^{\infty}(-1)^n\dfrac{n+3}{(n+1)^2} is to be approximated by partial sums. Explain whether the sequence bn=n+3(n+1)2b_n=\dfrac{n+3}{(n+1)^2} is eventually decreasing, and state whether the alternating series error bound may be applied.

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